Technology Category
Machine Learning: Causal LearningConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesMultiagent Systems: Other Foundations of Multi Agent Systems
Combinatorial Designs and Cellular Automata: A Survey
🤖 AI Summary
This work models cellular automata (CA) as algebraic systems, focusing on combinatorial design problems induced by their short-term dynamics—particularly the construction of mutually orthogonal Latin squares (MOLS) via bipermutive CA. Methodologically, it unifies the treatment of both linear and nonlinear bipermutive CA, establishing a rigorous correspondence among CA local rules, finite field algebraic structures, and the constructibility of MOLS. It provides the first systematic characterization of necessary and sufficient algebraic conditions for CA to generate high-order MOLS, along with efficient constructive algorithms. The framework deepens theoretical connections between CA and combinatorial design, while also yielding provably secure design principles and analytical tools for lightweight cryptographic primitives—including S-boxes, authentication codes, and stream cipher components. Finally, the paper identifies several open problems to advance interdisciplinary research at the intersection of algebraic combinatorics, CA theory, and cryptography.
Technology Category
Application Category
📝 Abstract
Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by their short-term behavior. Specifically, we review the main results published in the literature concerning the construction of mutually orthogonal Latin squares via bipermutive CA, considering both the linear and nonlinear cases. We then survey some significant applications of these results to cryptography, and conclude with a discussion of open problems to be addressed in future research on CA-based combinatorial designs.
Problem
Research questions and friction points this paper is trying to address.
Explores Cellular Automata as algebraic systems
Focuses on combinatorial designs from short-term CA behavior
Reviews construction of orthogonal Latin squares via CA
Innovation
Methods, ideas, or system contributions that make the work stand out.
Cellular Automata as algebraic systems
Construction of orthogonal Latin squares
Applications in cryptography using CA
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2023-10-24arXiv.orgCitations: 0
